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Simplifying -2.7t2 + 50t + 6.5 = 10 Reorder the terms: 6.5 + 50t + -2.7t2 = 10 Solving 6.5 + 50t + -2.7t2 = 10 Solving for variable 't'. Reorder the terms: 6.5 + -10 + 50t + -2.7t2 = 10 + -10 Combine like terms: 6.5 + -10 = -3.5 -3.5 + 50t + -2.7t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -3.5 + 50t + -2.7t2 = 0 Begin completing the square. Divide all terms by -2.7 the coefficient of the squared term: Divide each side by '-2.7'. 1.296296296 + -18.51851852t + t2 = 0 Move the constant term to the right: Add '-1.296296296' to each side of the equation. 1.296296296 + -18.51851852t + -1.296296296 + t2 = 0 + -1.296296296 Reorder the terms: 1.296296296 + -1.296296296 + -18.51851852t + t2 = 0 + -1.296296296 Combine like terms: 1.296296296 + -1.296296296 = 0.000000000 0.000000000 + -18.51851852t + t2 = 0 + -1.296296296 -18.51851852t + t2 = 0 + -1.296296296 Combine like terms: 0 + -1.296296296 = -1.296296296 -18.51851852t + t2 = -1.296296296 The t term is -18.51851852t. Take half its coefficient (-9.25925926). Square it (85.73388204) and add it to both sides. Add '85.73388204' to each side of the equation. -18.51851852t + 85.73388204 + t2 = -1.296296296 + 85.73388204 Reorder the terms: 85.73388204 + -18.51851852t + t2 = -1.296296296 + 85.73388204 Combine like terms: -1.296296296 + 85.73388204 = 84.437585744 85.73388204 + -18.51851852t + t2 = 84.437585744 Factor a perfect square on the left side: (t + -9.25925926)(t + -9.25925926) = 84.437585744 Calculate the square root of the right side: 9.18899264 Break this problem into two subproblems by setting (t + -9.25925926) equal to 9.18899264 and -9.18899264.Subproblem 1
t + -9.25925926 = 9.18899264 Simplifying t + -9.25925926 = 9.18899264 Reorder the terms: -9.25925926 + t = 9.18899264 Solving -9.25925926 + t = 9.18899264 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.25925926' to each side of the equation. -9.25925926 + 9.25925926 + t = 9.18899264 + 9.25925926 Combine like terms: -9.25925926 + 9.25925926 = 0.00000000 0.00000000 + t = 9.18899264 + 9.25925926 t = 9.18899264 + 9.25925926 Combine like terms: 9.18899264 + 9.25925926 = 18.4482519 t = 18.4482519 Simplifying t = 18.4482519Subproblem 2
t + -9.25925926 = -9.18899264 Simplifying t + -9.25925926 = -9.18899264 Reorder the terms: -9.25925926 + t = -9.18899264 Solving -9.25925926 + t = -9.18899264 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.25925926' to each side of the equation. -9.25925926 + 9.25925926 + t = -9.18899264 + 9.25925926 Combine like terms: -9.25925926 + 9.25925926 = 0.00000000 0.00000000 + t = -9.18899264 + 9.25925926 t = -9.18899264 + 9.25925926 Combine like terms: -9.18899264 + 9.25925926 = 0.07026662 t = 0.07026662 Simplifying t = 0.07026662Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.4482519, 0.07026662}
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